Analytical and numerical studies of phases of systems with spatially modulated symmetries

In recent years, systems with unconventional symmetries have attracted a lot of attention due to the wealth of exotic phenomena they display. In particular, the role of multipole-moment and subsystem symmetries have been explored extensively. Both of these have been shown to lead to exotic low-energy features including fracton phases of matter, fractal quantum criticality, Bose surfaces and UV/IR-mixing among other phenomena. In this talk, we will study a family of bosonic one-dimensional models, which conserve

certain finite-momentum Fourier components of the particle density, although not the total particle number itself. We will discuss the rich diagram of these systems, which can include two different types of gapless phases and "modulated" Mott-insulating lobes. If time permits, we will discuss their effects in higher dimensions.